Question

4. A regular hexagon is composed of 12 congruent 30-60-90 triangles. If the length of the hypotenuse of one of those triangles is 18 square root of 3 what is the perimeter of the hexagon?

Answer 1

We can divide a regular hexagon into 6 equilateral triangles or 12 30-60-90 right triangles. Since the hypotenuse of one of the triangles is the side of one of the equilateral triangles of the side of the hexagon, we will calculate the area of one of the equilateral triangles using the formula
A = (s^2 sqrt(3))/4 = {[18 sqrt(3)]^2(sqrt(3)}/4 = [972 sqrt(3)]/4 = 243 sqrt(3)
Since the hexagon has 6 identical (congruent) equilateral triangles, the area of the hexagon is [243 sqrt(3)](6) = 1458 sqrt(3)